考虑横向剪切变形矩形底中厚扁壳的屈曲研究  

Buckling of rectangular moderately thick shallow shells by transverse shearing deformation

作　　者：黄会荣[1] 朱怡婕[1] 赵岩[1] 张海霞[2] 

机构地区：[1]西安建筑科技大学机电工程学院,西安710055 [2]山东省泰安市建筑设计院,泰安271000

出　　处：《应用力学学报》2013年第3期361-366,474-475,共6页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金(50878181);陕西省教育厅专项基金(11JK0958)

摘　　要：基于考虑横向剪切变形直角坐标下矩形中厚扁壳的几何方程、本构关系、平衡方程,建立了关于三个中面位移和两个中面转角为独立变量的矩形中厚扁壳小挠度屈曲的基本微分方程。该方程可退化为矩形中厚板屈曲的基本微分方程,从而说明本文推导过程的正确性及一般性。文中矩形中厚扁壳小挠度屈曲的基本微分方程是一组耦合的变系数二阶偏微分方程,对常曲率扁壳使用双重三角级数并将其作为广义坐标对该方程组进行解耦,进一步建立中厚扁壳小挠度屈曲的特征方程,并得到了简支矩形中厚壳屈曲的临界荷载表达式,最后获得了其屈曲的临界荷载曲线及其相应的临界荷载值。该临界荷载曲线及其相应的临界荷载值可以退化为矩形中厚板的临界荷载曲线及临界荷载值。结果表明:本文提出的算法求解过程简便,矩形中厚扁壳临界荷载收敛较快。Fundamental differential equations of the rectangular moderately thick shallow shells small-deflection buckling concerning five independent variables,i.e.three middle surface displacements and two middle surface intersection angles are established based on the geometric equations,constitutive relations and equilibrium equations considering transverse shear deformation.The equations can degenerate to the basic differential equations of the rectangular moderately thick plates buckling,which demonstrates the validity and generality of the solving process.In this paper,the fundamental differential equation is a second order partial differential equation with variable coefficients,the double trigonometric series is used to solve the shallow shell equations with the constant curvature,and it also decouples the equations as a generalized coordinates,then the characteristic equation of the rectangular moderately thick shallow shells small-deflection buckling and the critical load expression of the simply supported rectangular moderately thick shallow shells buckling are obtained.Finally,the curves of critical load and the corresponding critical load values can degenerate to the curves of critical load and corresponding critical load values of the rectangular moderately thick plates.The results indicate that the solving process is simple and convenient,and the convergence of critical load is rather fast.

关 键 词：横向剪切变形 矩形底中厚扁壳 小挠度屈曲 基本微分方程 双重三角级数 特征方程 临界荷载 

分 类 号：TU33[建筑科学—结构工程]